A000779 - OEIS

%I #29 Sep 08 2022 08:44:28

%S 1,4,22,162,1506,16950,224190,3408930,58596930,1123663590,23782729950,

%T 550718680050,13849716607650,375904338960150,10952237584237950,

%U 340947694234397250,11294123783425733250,396665528378000631750

%N a(n) = 2*(2n-1)!!-(n-1)!*2^(n-1), where (2n-1)!! is A001147(n).

%H Nathaniel Johnston, <a href="/A000779/b000779.txt">Table of n, a(n) for n = 1..250</a>

%H J. R. Stembridge, <a href="http://dx.doi.org/10.1090/S0002-9947-97-01805-9">Some combinatorial aspects of reduced words in finite Coxeter groups</a>, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.

%p seq(2*doublefactorial(2*n-1)-(n-1)!*2^(n-1), n=1..18); # _Nathaniel Johnston_, Jun 23 2011

%t Table[2*(2n-1)!! - (n-1)!*2^(n-1), {n, 1, 20}] (* _Jean-François Alcover_, Feb 11 2016 *)

%o (Magma) A001147:=func< n | n eq 0 select 1 else &*[ k: k in [1..2*n-1 by 2] ] >; [ 2*A001147(n)-Factorial(n-1)*2^(n-1): n in [1..20] ]; // _Klaus Brockhaus_, Jun 22 2011

%Y Cf. A001147.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Jun 13 2011